A and B can do a piece of work in 12 days and 20 days, respectively. Both work for 3 days and then A leaves. How long (in days) will B take to complete the remaining work?
12
Combined rate of A and B: \(\tfrac1{12}+\tfrac1{20} = \tfrac{5+3}{60} = \tfrac{8}{60} = \tfrac{2}{15}\) per day.
Work done in 3 days: \(3\times\tfrac{2}{15} = \tfrac{6}{15} = \tfrac25\).
Remaining work: \(1-\tfrac25 = \tfrac35\).
Time for B alone to finish: \(\dfrac{3/5}{1/20} = 12\) days.
Hence, B will take 12 days to complete the remaining work.
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